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+{{Technical data page}}
 The '''cloudy clan''' tempers out the [[cloudy comma]], 16807/16384, thus splitting the octave into 5 equal parts and mapping the harmonic 7 to 4\5.
-Temperaments discussed elsewhere are [[Archytas clan #Blacksmith|blacksmith]], [[Meantone family #Cloudtone|cloudtone]], [[Pental family #Pentacloud|pentacloud]] and [[Qintosec family #Sengasec|sengasec]].
+Temperaments discussed elsewhere are:
+* [[Blacksmith]] (+28/27 or 49/48) → [[Limmic temperaments #Blacksmith|Limmic temperaments]]
+* [[Cloudtone]] (+81/80) → [[Meantone family #Cloudtone|Meantone family]]
+* [[Pental (temperament)|Pental]] (+245/243) → [[Pental family #Pentacloud|Pental family]]
+* [[Sengasec]] (+686/675) → [[Quintosec family #Sengasec|Quintosec family]]
+* [[Warlock]] (+3125/3072) → [[Magic family #Warlock|Magic family]]
-== Coblack  ==
+== Coblack ==
-{{see also|Trisedodge family #Coblack}}
+{{See also| Trisedodge family #Coblack }}
-Subgroup: 2.3.5.7
+In addition to the [[cloudy comma]], the coblack temperament tempers out the [[126/125|starling comma (126/125)]]. Coblack was named by [[Petr Pařízek]] in 2011, who considered it a counterpart of [[blacksmith]]<ref>[https://yahootuninggroupsultimatebackup.github.io/tuning/topicId_101780.html Yahoo! Tuning Group | ''Suggested names for the unclasified temperaments'']</ref>.
+[[Subgroup]]: 2.3.5.7
 [[Comma list]]: 126/125, 16807/16384
-[[Mapping]]: [{{val| 5 1 7 14 }}, {{val| 0 3 2 0 }}]
+{{Mapping|legend=1| 5 1 7 14 | 0 3 2 0 }}
-{{Multival|legend=1| 15 10 0 -19 -42 -28 }}
-[[POTE generator]]: ~21/20 = 73.044
+[[Optimal tuning]]s:
+* [[CTE]]: ~8/7 = 1\5, ~48/35 = 553.8429 (~21/20 = 73.8429)
+* [[POTE]]: ~8/7 = 1\5, ~48/35 = 553.044 (~21/20 = 73.044)
-{{Val list|legend=1| 15, 35, 50, 65, 115d }}
+{{Optimal ET sequence|legend=1| 15, 35, 50, 65, 115d }}
 [[Badness]]: 0.107282
-=== 11-limit  ===
+=== 11-limit ===
 Subgroup: 2.3.5.7.11
 Comma list: 126/125, 245/242, 385/384
-Mapping: [{{val| 5 1 7 14 15 }}, {{val| 0 3 2 0 1 }}]
+Mapping: {{mapping| 5 1 7 14 15 | 0 3 2 0 1 }}
-POTE generator: ~21/20 = 73.264
+Optimal tunings:
+* CTE: ~8/7 = 1\5, ~11/8 = 553.7951 (~21/20 = 73.7951)
+* POTE: ~8/7 = 1\5, ~11/8 = 553.264 (~21/20 = 73.264)
-Vals: {{Val list| 15, 35, 50, 65, 115d }}
+Optimal ET sequence: {{Optimal ET sequence| 15, 35, 50, 65, 115d }}
 Badness: 0.045070
-== Decic  ==
+== Decic ==
-The ''decic'' temperament (10&amp;50, named by [[User:Xenllium|Xenllium]]) tempers out the [[cloudy comma]], 16807/16384 and the [[225/224|marvel comma]], 225/224 in the 7-limit, as well as the [[15/14ths equal temperament|linus comma]], {{monzo|11 -10 -10 10}}. This temperament is supported by [[10edo|10]], [[50edo|50]], and [[60edo|60]] EDOs, and can be extended naturally to the 11-, 13-, and 17-limit by adding 385/384, 105/104, and 170/169 to the comma list in this order.
+{{Main| Decic }}
+The ''decic'' temperament (10 &amp; 50) tempers out the [[cloudy comma]], 16807/16384 and the [[225/224|marvel comma]], 225/224 in the 7-limit, as well as the [[linus comma]], {{monzo| 11 -10 -10 10 }}. This temperament is supported by [[10edo|10-]], [[50edo|50-]], and [[60edo]], and can be extended naturally to the 11-, 13-, and 17-limit by adding 385/384, 105/104, and 170/169 to the comma list in this order.
-Subgroup: 2.3.5.7
+[[Subgroup]]: 2.3.5.7
 [[Comma list]]: 225/224, 16807/16384
-[[Mapping]]: [{{val| 10 0 39 28 }}, {{val| 0 1 -1 0 }}]
+{{Mapping|legend=1| 10 0 39 28 | 0 1 -1 0 }}
-Mapping generators: ~15/14, ~3
-{{Multival|legend=1| 10 -10 0 -39 -28 28 }}
-[[POTE generator]]: ~3/2 = 698.696
+: mapping generators: ~15/14, ~3
-[[Tuning ranges]]:
+[[Optimal tuning]] ([[POTE]]): ~15/14 = 1\10, ~3/2 = 698.696 (~49/48 = 21.304)
-* [[diamond monotone]] range: ~3/2 = [696.000, 700.000] (29\50 to 35\60)
-* [[diamond tradeoff]] range: ~3/2 = [693.129, 702.512]
-* diamond monotone and tradeoff range: ~3/2 = [696.000, 700.000]
-{{Val list|legend=1| 10, 50, 60, 110d, 170cdd }}
+{{Optimal ET sequence|legend=1| 10, 30b, 40, 50, 60, 110d, 170cdd }}
 [[Badness]]: 0.089135
-=== 11-limit  ===
+=== 11-limit ===
 Subgroup: 2.3.5.7.11
 Comma list: 225/224, 385/384, 3087/3025
-Mapping: [{{val| 10 0 39 28 3 }}, {{val| 0 1 -1 0 2 }}]
+Mapping: {{mapping| 10 0 39 28 3 | 0 1 -1 0 2 }}
-Mapping generators: ~15/14, ~3
-POTE generator: ~3/2 = 696.791
+: mapping generators: ~15/14, ~3
-Tuning ranges:
+Optimal tuning (POTE): ~15/14 = 1\10, ~3/2 = 696.791 (~56/55 = 23.209)
-* [[diamond monotone]] range: ~3/2 = [696.000, 700.000] (29\50 to 35\60)
-* [[diamond tradeoff]] range: ~3/2 = [689.363, 702.512]
-* diamond monotone and tradeoff range: ~3/2 = [696.000, 700.000]
-Vals: {{Val list| 10, 50, 160bcdd, 210bcddde, 260bbcddde, 310bbcdddde }}
+{{Optimal ET sequence|legend=1| 10, 30be, 40, 50 }}
 Badness: 0.063900
-=== 13-limit  ===
+==== 13-limit ====
 Subgroup: 2.3.5.7.11.13
 Comma list: 105/104, 144/143, 196/195, 2200/2197
-Mapping: [{{val| 10 0 39 28 3 37 }}, {{val| 0 1 -1 0 2 0 }}]
+Mapping: {{mapping| 10 0 39 28 3 37 | 0 1 -1 0 2 0 }}
-Mapping generators: ~14/13, ~3
-POTE generator: ~3/2 = 696.993
+: mapping generators: ~14/13, ~3
-Tuning ranges:
+Optimal tuning (POTE): ~15/14 = 1\10, ~3/2 = 696.993 (~78/77 = 23.007)
-* [[diamond monotone]] range: ~3/2 = [696.000, 700.000] (29\50 to 35\60)
-* [[diamond tradeoff]] range: ~3/2 = [689.363, 702.512]
-* diamond monotone and tradeoff range: ~3/2 = [696.000, 700.000]
-Vals: {{Val list| 10, 50, 160bcdd, 210bcddde, 260bbcddde }}
+{{Optimal ET sequence|legend=1| 10, 30be, 40, 50 }}
 Badness: 0.036880
-=== 17-limit  ===
+==== 17-limit ====
 Subgroup: 2.3.5.7.11.13.17
 Comma list: 105/104, 144/143, 170/169, 196/195, 221/220
-Mapping: [{{val| 10 0 39 28 3 37 25 }}, {{val| 0 1 -1 0 2 0 1 }}]
+Mapping: {{mapping| 10 0 39 28 3 37 25 | 0 1 -1 0 2 0 1 }}
+: mapping generators: ~14/13, ~3
+Optimal tuning (POTE): ~15/14 = 1\10, ~3/2 = 697.085 (~78/77 = 22.915)
+{{Optimal ET sequence|legend=1| 10, 30beg, 40, 50 }}
+Badness: 0.025064
+=== Splendecic ===
+''Splendecic'' (10e &amp; 50) is an alternative extension of decic, tempering out 1617/1600, 2401/2376 and 4375/4356 in the 11-limit. As a temperament of the [[Marvel family #Fantastic|fantastic rank-3 temperament]], its name is a portmanteau of "[[wiktionary:splendid|splendid]]" (synonym of "[[wiktionary:fantastic|fantastic]]") and "decic".
+Subgroup: 2.3.5.7.11
+Comma list: 225/224, 1617/1600, 2401/2376
+Mapping: {{mapping| 10 0 39 28 82 | 0 1 -1 0 -3 }}
+Optimal tuning (POTE): ~15/14 = 1\10, ~3/2 = 698.518 (~99/98 = 21.482)
+{{Optimal ET sequence|legend=1| 10e, 30bee, 40e, 50, 60e, 110de }}
+Badness: 0.059802
+==== 13-limit ====
+Subgroup: 2.3.5.7.11.13
+Comma list: 105/104, 196/195, 1001/1000, 1188/1183
+Mapping: {{mapping| 10 0 39 28 82 37 | 0 1 -1 0 -3 0 }}
+Optimal tuning (POTE): ~15/14 = 1\10, ~3/2 = 698.365 (~91/90 = 21.635)
+{{Optimal ET sequence|legend=1| 10e, 30bee, 40e, 50, 60e, 110de }}
+Badness: 0.037989
+==== 17-limit ====
+Subgroup: 2.3.5.7.11.13.17
+Comma list: 105/104, 170/169, 196/195, 289/288, 375/374
+Mapping: {{mapping| 10 0 39 28 82 37 25 | 0 1 -1 0 -3 0 1 }}
+Optimal tuning (POTE): ~15/14 = 1\10, ~3/2 = 698.375 (~91/90 = 21.625)
+{{Optimal ET sequence|legend=1| 10e, 30beeg, 40e, 50, 60e, 110deg }}
+Badness: 0.026050
+=== Prodecic ===
+''Prodecic'' (10 &amp; 50e) is an alternative extension of decic, tempering out 441/440, 1375/1372 and 4375/4356 in the 11-limit. As a temperament of the [[Marvel family #Prodigy|prodigy rank-3 temperament]], its name is a portmanteau of "[[wiktionary:prodigy|prodigy]]" and "decic".
+Subgroup: 2.3.5.7.11
-Mapping generators: ~14/13, ~3
+Comma list: 225/224, 441/440, 5929/5832
-POTE generator: ~3/2 = 697.085
+Mapping: {{mapping| 10 0 39 28 -13 | 0 1 -1 0 3 }}
-Tuning ranges:
+Optimal tuning (POTE): ~15/14 = 1\10, ~3/2 = 700.210 (~55/54 = 19.790)
-* [[diamond monotone]] range: ~3/2 = [696.000, 700.000] (29\50 to 35\60)
-* [[diamond tradeoff]] range: ~3/2 = [689.363, 704.955]
-* diamond monotone and tradeoff range: ~3/2 = [696.000, 700.000]
-Vals: {{Val list| 10, 50, 160bcddg, 210bcdddegg }}
+{{Optimal ET sequence|legend=1| 10, 40ee, 50e, 60e }}
-Badness: 0.025064
+Badness: 0.066600
+==== 13-limit ====
+Subgroup: 2.3.5.7.11.13
+Comma list: 105/104, 196/195, 275/273, 5929/5832
+Mapping: {{mapping| 10 0 39 28 -13 37 | 0 1 -1 0 3 0 }}
+Optimal tuning (POTE): ~15/14 = 1\10, ~3/2 = 700.503 (~91/90 = 19.497)
+{{Optimal ET sequence|legend=1| 10, 40ee, 50e, 60e }}
+Badness: 0.041788
+==== 17-limit ====
+Subgroup: 2.3.5.7.11.13.17
+Comma list: 105/104, 154/153, 170/169, 196/195, 289/288
+Mapping: {{mapping| 10 0 39 28 -13 37 25 | 0 1 -1 0 3 0 1 }}
+Optimal tuning (POTE): ~15/14 = 1\10, ~3/2 = 700.474 (~91/90 = 19.526)
+{{Optimal ET sequence|legend=1| 10, 40ee, 50e, 60e }}
+Badness: 0.027590
+== Pentadecal ==
+: ''For the 5-limit version of this temperament, see [[High badness temperaments #Pentadecal]].''
+The ''pentadecal'' temperament tempers out the 15-5/3-comma (Quintriyo, pentadecatonic minor thirds comma), {{monzo|-11 -15 15}}. This temperament can be described as 15&amp;60 temperament, tempering out the [[cloudy comma]], 16807/16384 and the [[875/864|keema]], 875/864 in the 7-limit.
+[[Subgroup]]: 2.3.5.7
+[[Comma list]]: 875/864, 16807/16384
+{{Mapping|legend=1| 15 0 11 42 | 0 1 1 0 }}
+: mapping generators: ~21/20, ~3
+[[Optimal tuning]] ([[POTE]]): ~21/20 = 1\15, ~3/2 = 700.223 (~126/125 = 19.777)
+{{Optimal ET sequence|legend=1| 15, 45, 60 }}
+[[Badness]]: 0.114833
+=== 11-limit ===
+Subgroup: 2.3.5.7.11
+Comma list: 100/99, 385/384, 1372/1331
+Mapping: {{mapping| 15 0 11 42 52 | 0 1 1 0 0 }}
+: mapping generators: ~21/20, ~3
+Optimal tuning (POTE): ~21/20 = 1\15, ~3/2 = 702.733 (~56/55 = 17.267)
+{{Optimal ET sequence|legend=1| 15, 45, 60, 75de, 135de }}
+Badness: 0.077420
+==== 13-limit ====
+Subgroup: 2.3.5.7.11.13
+Comma list: 100/99, 105/104, 144/143, 1372/1331
+Mapping: {{mapping| 15 0 11 42 52 8 | 0 1 1 0 0 2 }}
+: mapping generators: ~21/20, ~3
+Optimal tuning (POTE): ~21/20 = 1\15, ~3/2 = 701.715 (~91/90 = 18.285)
+{{Optimal ET sequence|legend=1| 15, 45f, 60, 135de, 195cddee }}
+Badness: 0.051740
+=== Quindecal ===
+Subgroup: 2.3.5.7.11
+Comma list: 121/120, 441/440, 875/864
+Mapping: {{mapping| 15 0 11 42 28 | 0 1 1 0 1 }}
+: mapping generators: ~21/20, ~3
+Optimal tuning (POTE): ~21/20 = 1\15, ~3/2 = 700.318 (~126/125 = 19.682)
+{{Optimal ET sequence|legend=1| 15, 45e, 60e }}
+Badness: 0.044405
+==== 13-limit ====
+Subgroup: 2.3.5.7.11.13
+Comma list: 121/120, 196/195, 352/351, 875/864
+Mapping: {{mapping| 15 0 11 42 28 103 | 0 1 1 0 1 -2 }}
+: mapping generators: ~21/20, ~3
+Optimal tuning (POTE): ~21/20 = 1\15, ~3/2 = 701.647 (~65/64 = 18.353)
+{{Optimal ET sequence|legend=1| 15f, 45e, 60e }}
+Badness: 0.055361
+== Quinkee ==
+The ''quinkee'' temperament (15 &amp; 40) has a period of 1/5 octave and tempers out the keega (1029/1000), and from this it derives its name.
+[[Subgroup]]: 2.3.5.7
+[[Comma list]]: 1029/1000, 6144/6125
+{{Mapping|legend=1| 5 9 12 14 | 0 -3 -1 0 }}
+[[Optimal tuning]] ([[POTE]]): ~8/7 = 1\5, ~5/4 = 393.439 (~25/24 = 86.561)
+{{Optimal ET sequence|legend=1| 15, 40, 55, 125cd, 180ccdd }}
+[[Badness]]: 0.184222
+=== 11-limit ===
+Subgroup: 2.3.5.7.11
+Comma list: 121/120, 176/175, 1029/1000
+Mapping: {{mapping| 5 9 12 14 18 | 0 -3 -1 0 -2 }}
+Optimal tuning (POTE): ~8/7 = 1\5, ~5/4 = 393.438 (~22/21 = 86.562)
+{{Optimal ET sequence|legend=1| 15, 40, 55, 125cd, 180ccdde }}
+Badness: 0.065192
+=== 13-limit ===
+Subgroup: 2.3.5.7.11.13
+Comma list: 66/65, 105/104, 121/120, 637/625
+Mapping: {{mapping| 5 9 12 14 18 20 | 0 -3 -1 0 -2 -4 }}
+Optimal tuning (POTE): ~8/7 = 1\5, ~5/4 = 392.798 (~22/21 = 87.202)
+{{Optimal ET sequence|legend=1| 15, 40, 55 }}
+Badness: 0.048440
+== Notes ==
-[[Category:Regular temperament theory]]
+[[Category:Temperament clans]]
-[[Category:Temperament clan]]
+[[Category:Pages with mostly numerical content]]
-[[Category:Cloudy]]
+[[Category:Cloudy clan| ]] <!-- main article -->
+[[Category:Cloudy| ]] <!-- key article -->
 [[Category:Rank 2]]

Cloudy clan: Difference between revisions